///////////////////////////////////////
// Implements:
//   double pow(double x, double y);
///////////////////////////////////////
// Notes:
//   This is taken from newlib.
// @nolint

/*
 * ====================================================
 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
 *
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#include <stdint.h>
#include <pblibc_private.h>

/* __ieee754_pow(x,y) return x**y
 *
 *          n
 * Method:  Let x =  2   * (1+f)
 *  1. Compute and return log2(x) in two pieces:
 *    log2(x) = w1 + w2,
 *     where w1 has 53-24 = 29 bit trailing zeros.
 *  2. Perform y*log2(x) = n+y' by simulating multi-precision
 *     arithmetic, where |y'|<=0.5.
 *  3. Return x**y = 2**n*exp(y'*log2)
 *
 * Special cases:
 *  1.  (anything) ** 0  is 1
 *  2.  (anything) ** 1  is itself
 *  3a. (anything) ** NAN is NAN except
 *  3b. +1         ** NAN is 1
 *  4.  NAN ** (anything except 0) is NAN
 *  5.  +-(|x| > 1) **  +INF is +INF
 *  6.  +-(|x| > 1) **  -INF is +0
 *  7.  +-(|x| < 1) **  +INF is +0
 *  8.  +-(|x| < 1) **  -INF is +INF
 *  9.  +-1         ** +-INF is 1
 *  10. +0 ** (+anything except 0, NAN)               is +0
 *  11. -0 ** (+anything except 0, NAN, odd integer)  is +0
 *  12. +0 ** (-anything except 0, NAN)               is +INF
 *  13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
 *  14. -0 ** (odd integer) = -( +0 ** (odd integer) )
 *  15. +INF ** (+anything except 0,NAN) is +INF
 *  16. +INF ** (-anything except 0,NAN) is +0
 *  17. -INF ** (anything)  = -0 ** (-anything)
 *  18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
 *  19. (-anything except 0 and inf) ** (non-integer) is NAN
 *
 * Accuracy:
 *  pow(x,y) returns x**y nearly rounded. In particular
 *      pow(integer,integer)
 *  always returns the correct integer provided it is
 *  representable.
 *
 * Constants :
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

static const double
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
zero    =  0.0,
one =  1.0,
two =  2.0,
two53 =  9007199254740992.0,  /* 0x43400000, 0x00000000 */
huge  =  1.0e300,
tiny    =  1.0e-300,
  /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

typedef union
{
  double value;
  struct
  {
    uint32_t lsw;
    uint32_t msw;
  } parts;
} ieee_double_shape_type;

#define EXTRACT_WORDS(ix0,ix1,d)        \
do {                \
  ieee_double_shape_type ew_u;          \
  ew_u.value = (d);           \
  (ix0) = ew_u.parts.msw;         \
  (ix1) = ew_u.parts.lsw;         \
} while (0)

/* Get the more significant 32 bit int from a double.  */

#define GET_HIGH_WORD(i,d)          \
do {                \
  ieee_double_shape_type gh_u;          \
  gh_u.value = (d);           \
  (i) = gh_u.parts.msw;           \
} while (0)

/* Get the less significant 32 bit int from a double.  */

#define GET_LOW_WORD(i,d)         \
do {                \
  ieee_double_shape_type gl_u;          \
  gl_u.value = (d);           \
  (i) = gl_u.parts.lsw;           \
} while (0)

/* Set the more significant 32 bits of a double from an int.  */

#define SET_HIGH_WORD(d,v)          \
do {                \
  ieee_double_shape_type sh_u;          \
  sh_u.value = (d);           \
  sh_u.parts.msw = (v);           \
  (d) = sh_u.value;           \
} while (0)

/* Set the less significant 32 bits of a double from an int.  */

#define SET_LOW_WORD(d,v)         \
do {                \
  ieee_double_shape_type sl_u;          \
  sl_u.value = (d);           \
  sl_u.parts.lsw = (v);           \
  (d) = sl_u.value;           \
} while (0)

double pow(double x, double y)
{
  double z,ax,z_h,z_l,p_h,p_l;
  double y1,t1,t2,r,s,t,u,v,w;
  int32_t i,j,k,yisint,n;
  int32_t hx,hy,ix,iy;
  uint32_t lx,ly;

  EXTRACT_WORDS(hx,lx,x);
  EXTRACT_WORDS(hy,ly,y);
  ix = hx&0x7fffffff;  iy = hy&0x7fffffff;

    /* y==zero: x**0 = 1 */
  if((iy|ly)==0) return one;

    /* x|y==NaN return NaN unless x==1 then return 1 */
  if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
     iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) {
      if(((ix-0x3ff00000)|lx)==0) return one;
      else return __builtin_nan("");
  }

    /* determine if y is an odd int when x < 0
     * yisint = 0 ... y is not an integer
     * yisint = 1 ... y is an odd int
     * yisint = 2 ... y is an even int
     */
  yisint  = 0;
  if(hx<0) {
      if(iy>=0x43400000) yisint = 2; /* even integer y */
      else if(iy>=0x3ff00000) {
    k = (iy>>20)-0x3ff;    /* exponent */
    if(k>20) {
        j = ly>>(52-k);
        if((uint32_t)(j<<(52-k))==ly) yisint = 2-(j&1);
    } else if(ly==0) {
        j = iy>>(20-k);
        if((j<<(20-k))==iy) yisint = 2-(j&1);
    }
      }
  }

    /* special value of y */
  if(ly==0) {
      if (iy==0x7ff00000) { /* y is +-inf */
          if(((ix-0x3ff00000)|lx)==0)
        return one;   /* +-1**+-inf = 1 */
          else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
        return (hy>=0)? y: zero;
          else      /* (|x|<1)**-,+inf = inf,0 */
        return (hy<0)?-y: zero;
      }
      if(iy==0x3ff00000) {  /* y is  +-1 */
    if(hy<0) return one/x; else return x;
      }
      if(hy==0x40000000) return x*x; /* y is  2 */
      if(hy==0x3fe00000) {  /* y is  0.5 */
    if(hx>=0) /* x >= +0 */
    return __builtin_sqrt(x);
      }
  }

  ax   = __builtin_fabs(x);
    /* special value of x */
  if(lx==0) {
      if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
    z = ax;     /*x is +-0,+-inf,+-1*/
    if(hy<0) z = one/z; /* z = (1/|x|) */
    if(hx<0) {
        if(((ix-0x3ff00000)|yisint)==0) {
      z = (z-z)/(z-z); /* (-1)**non-int is NaN */
        } else if(yisint==1)
      z = -z;   /* (x<0)**odd = -(|x|**odd) */
    }
    return z;
      }
  }

    /* (x<0)**(non-int) is NaN */
    /* REDHAT LOCAL: This used to be
  if((((hx>>31)+1)|yisint)==0) return (x-x)/(x-x);
       but ANSI C says a right shift of a signed negative quantity is
       implementation defined.  */
  if(((((uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);

    /* |y| is huge */
  if(iy>0x41e00000) { /* if |y| > 2**31 */
      if(iy>0x43f00000){  /* if |y| > 2**64, must o/uflow */
    if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
    if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
      }
  /* over/underflow if x is not close to one */
      if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
      if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
  /* now |1-x| is tiny <= 2**-20, suffice to compute
     log(x) by x-x^2/2+x^3/3-x^4/4 */
      t = ax-1;   /* t has 20 trailing zeros */
      w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
      u = ivln2_h*t;  /* ivln2_h has 21 sig. bits */
      v = t*ivln2_l-w*ivln2;
      t1 = u+v;
      SET_LOW_WORD(t1,0);
      t2 = v-(t1-u);
  } else {
      double s2,s_h,s_l,t_h,t_l;
      n = 0;
  /* take care subnormal number */
      if(ix<0x00100000)
    {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
      n  += ((ix)>>20)-0x3ff;
      j  = ix&0x000fffff;
  /* determine interval */
      ix = j|0x3ff00000;    /* normalize ix */
      if(j<=0x3988E) k=0;   /* |x|<sqrt(3/2) */
      else if(j<0xBB67A) k=1; /* |x|<sqrt(3)   */
      else {k=0;n+=1;ix -= 0x00100000;}
      SET_HIGH_WORD(ax,ix);

  /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
      u = ax-bp[k];   /* bp[0]=1.0, bp[1]=1.5 */
      v = one/(ax+bp[k]);
      s = u*v;
      s_h = s;
      SET_LOW_WORD(s_h,0);
  /* t_h=ax+bp[k] High */
      t_h = zero;
      SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
      t_l = ax - (t_h-bp[k]);
      s_l = v*((u-s_h*t_h)-s_h*t_l);
  /* compute log(ax) */
      s2 = s*s;
      r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
      r += s_l*(s_h+s);
      s2  = s_h*s_h;
      t_h = 3.0+s2+r;
      SET_LOW_WORD(t_h,0);
      t_l = r-((t_h-3.0)-s2);
  /* u+v = s*(1+...) */
      u = s_h*t_h;
      v = s_l*t_h+t_l*s;
  /* 2/(3log2)*(s+...) */
      p_h = u+v;
      SET_LOW_WORD(p_h,0);
      p_l = v-(p_h-u);
      z_h = cp_h*p_h;   /* cp_h+cp_l = 2/(3*log2) */
      z_l = cp_l*p_h+p_l*cp+dp_l[k];
  /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
      t = (double)n;
      t1 = (((z_h+z_l)+dp_h[k])+t);
      SET_LOW_WORD(t1,0);
      t2 = z_l-(((t1-t)-dp_h[k])-z_h);
  }

  s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
  if(((((uint32_t)hx>>31)-1)|(yisint-1))==0)
      s = -one;/* (-ve)**(odd int) */

    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
  y1  = y;
  SET_LOW_WORD(y1,0);
  p_l = (y-y1)*t1+y*t2;
  p_h = y1*t1;
  z = p_l+p_h;
  EXTRACT_WORDS(j,i,z);
  if (j>=0x40900000) {        /* z >= 1024 */
      if(((j-0x40900000)|i)!=0)     /* if z > 1024 */
    return s*huge*huge;     /* overflow */
      else {
    if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
      }
  } else if((j&0x7fffffff)>=0x4090cc00 ) {  /* z <= -1075 */
      if(((j-0xc090cc00)|i)!=0)     /* z < -1075 */
    return s*tiny*tiny;   /* underflow */
      else {
    if(p_l<=z-p_h) return s*tiny*tiny;  /* underflow */
      }
  }
    /*
     * compute 2**(p_h+p_l)
     */
  i = j&0x7fffffff;
  k = (i>>20)-0x3ff;
  n = 0;
  if(i>0x3fe00000) {    /* if |z| > 0.5, set n = [z+0.5] */
      n = j+(0x00100000>>(k+1));
      k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
      t = zero;
      SET_HIGH_WORD(t,n&~(0x000fffff>>k));
      n = ((n&0x000fffff)|0x00100000)>>(20-k);
      if(j<0) n = -n;
      p_h -= t;
  }
  t = p_l+p_h;
  SET_LOW_WORD(t,0);
  u = t*lg2_h;
  v = (p_l-(t-p_h))*lg2+t*lg2_l;
  z = u+v;
  w = v-(z-u);
  t  = z*z;
  t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
  r  = (z*t1)/(t1-two)-(w+z*w);
  z  = one-(r-z);
  GET_HIGH_WORD(j,z);
  j += (n<<20);
  if((j>>20)<=0) z = __builtin_scalbn(z,(int)n);  /* subnormal output */
  else SET_HIGH_WORD(z,j);
  return s*z;
}
